Final answer:
The statement about a parallelogram having an axis of symmetry through its diagonals is false, but a vector can indeed form a right angle triangle with its components, and the Pythagorean theorem could be used to calculate a resultant vector at right angles.
Step-by-step explanation:
The statement 'A parallelogram has line symmetry and either diagonal is an axis of symmetry' is False. While a parallelogram does exhibit line symmetry, meaning that it can be divided into two mirror-image halves, it is not necessarily true that either diagonal forms an axis of symmetry. An axis of symmetry through a diagonal would mean that the two halves of the parallelogram reflected over that diagonal would match exactly, which is only true for a special type of parallelogram known as a rhombus. In general parallelograms, the diagonals are not axes of symmetry.
Regarding vectors, it is True that a vector can form the shape of a right angle triangle with its x and y components. This is a fundamental concept in vector addition where the original vector (the hypotenuse) and its x and y components (the legs) form a right angle triangle. The lengths of the sides can be calculated using trigonometric functions, as the x-component (Âx) is often represented as Âx = A cos θ and the y-component (Ây) as Ây = A sin θ, as provided in the reference information.
Furthermore, it is True that we can use the Pythagorean theorem to calculate the length of the resultant vector when adding two vectors that are at right angles to each other. This is because the resultant vector forms the hypotenuse of a right angle triangle with the two vectors as its legs.